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Optimization for scattering and radiation problems based on a stable FEM-FDTD hybrid method

Tomas Halleröd (Institutionen för signaler och system, Signalbehandling)
Göteborg : Chalmers University of Technology, 2007. ISBN: 978-91-7291-992-1.
[Doktorsavhandling]

In this thesis, a stable hybrid method combining the finite-element method (FEM) and the finite-difference time-domain (FDTD) scheme for Maxwell's equations in two dimensions with both electric and magnetic losses is presented. It combines the flexibility of the FEM with the efficiency of the FDTD scheme. The hybrid method time-step the Ampère's and Faraday's law and it is stable up to the Courant stability limit of the FDTD scheme. Numerical computations for smooth scatterers demonstrate second order convergence for the hybrid scheme. We apply the FEM-FDTD hybrid to shape and material optimization problems with the aim of reducing the radar cross section of an airfoil over a range of frequencies and incident angles. Efficient gradient optimization based on the adjoint formulation is employed. It is shown that optimization over a wide frequency band effectively suppresses corrugations and allows for a reduction in angular resolution and hence a reduced overall computational cost. Finally, the hybrid method is exploited in the pattern synthesis for conformal array antennas whereby effects such as mutual coupling are included. The objective function is a linear combination of two terms, expressing the deviation from a desired radiation pattern and the reflected power, respectively. The array excitation is expressed in terms of phase modes, which allow for convenient parameterization and control of the radiating modes. A gradient based optimization method is employed, which yields a radiation pattern similar to that obtained by Dolph-Chebyshev synthesis, but with a significantly reduced reflected power.

Nyckelord: finite element method, finite-difference time-domain, electric and magnetic losses, explicit-implicit time-stepping, scattering, shape and material optimization, array antennas, pattern synthesis



Denna post skapades 2007-09-17. Senast ändrad 2013-09-25.
CPL Pubid: 48264

 

Institutioner (Chalmers)

Institutionen för signaler och system, Signalbehandling (1900-2017)

Ämnesområden

Tillämpad matematik
Elektroteknik

Chalmers infrastruktur

Examination

Datum: 2007-10-12
Tid: 10:00
Lokal: Sal EB, Hörsalsvägen 11
Opponent: Bitr. professor Peter Meincke, Ørsted DTU ElectroScience, Technical University of Denmark

Ingår i serie

Doktorsavhandlingar vid Chalmers tekniska högskola. Ny serie 2673